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# geocdf

Geometric cumulative distribution function

## Syntax

y = geocdf(x,p)
y = geocdf(x,p,'upper')

## Description

y = geocdf(x,p) returns the cumulative distribution function (cdf) of the geometric distribution at each value in x using the corresponding probabilities in p. x and p can be vectors, matrices, or multidimensional arrays that all have the same size. A scalar input is expanded to a constant array with the same dimensions as the other input. The parameters in p must lie on the interval [0,1].

y = geocdf(x,p,'upper') returns the complement of the geometric distribution cdf at each value in x, using an algorithm that more accurately computes the extreme upper tail probabilities.

## Examples

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### Compute Geometric Distribution cdf

Suppose you toss a fair coin repeatedly, and a "success" occurs when the coin lands with heads facing up. What is the probability of observing three or fewer tails ("failures") before tossing a heads?

To solve, determine the value of the cumulative distribution function (cdf) for the geometric distribution at x equal to 3. The probability of success (tossing a heads) p in any given trial is 0.5.

```x = 3;
p = 0.5;
y = geocdf(x,p)
```
```y =

0.9375

```

The returned value of y indicates that the probability of observing three or fewer tails before tossing a heads is 0.9375.

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### Geometric Distribution cdf

The cumulative distribution function (cdf) of the geometric distribution is

$y=F\left(x|p\right)=1-{\left(1-p\right)}^{x+1}\text{\hspace{0.17em}};\text{\hspace{0.17em}}x=0,1,2,...\text{\hspace{0.17em}},$

where p is the probability of success, and x is the number of failures before the first success. The result y is the probability of observing up to x trials before a success, when the probability of success in any given trial is p.